How to solve (x-y)(x-10)+1=0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-y)(x-10)+1=0 | Equatix

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Question

$$(x-y)(x-10)+1=0$$

Solve for y

$y=-\frac{x^{2}-10x+1}{10-x}$
$x\neq 10$

Steps for Solving Linear Equation

Use the distributive property to multiply $x-y$ by $x-10$.

$$x^{2}-10x-yx+10y+1=0$$

Subtract $x^{2}$ from both sides. Anything subtracted from zero gives its negation.

$$-10x-yx+10y+1=-x^{2}$$

Add $10x$ to both sides.

$$-yx+10y+1=-x^{2}+10x$$

Subtract $1$ from both sides.

$$-yx+10y=-x^{2}+10x-1$$

Combine all terms containing $y$.

$$\left(-x+10\right)y=-x^{2}+10x-1$$

The equation is in standard form.

$$\left(10-x\right)y=-x^{2}+10x-1$$

Divide both sides by $-x+10$.

$$\frac{\left(10-x\right)y}{10-x}=\frac{-x^{2}+10x-1}{10-x}$$

Dividing by $-x+10$ undoes the multiplication by $-x+10$.

$$y=\frac{-x^{2}+10x-1}{10-x}$$

Show Solution

Solve for x (complex solution)

$x=\frac{\sqrt{\left(y-12\right)\left(y-8\right)}+y+10}{2}$
$x=\frac{-\sqrt{\left(y-12\right)\left(y-8\right)}+y+10}{2}$

Solve for x

$x=\frac{\sqrt{\left(y-12\right)\left(y-8\right)}+y+10}{2}$
$x=\frac{-\sqrt{\left(y-12\right)\left(y-8\right)}+y+10}{2}\text{, }y\leq 8\text{ or }y\geq 12$